JP7849705B2 - Method for measuring impedance parameters, and apparatus for measuring impedance parameters - Google Patents

Description

This technology relates to an impedance parameter measurement method and an impedance parameter measurement apparatus.

In recent years, with the spread of electric and hybrid vehicles, and with the proliferation of power generation devices such as solar and wind power, which have unstable power generation sources and require power leveling, the demand for lithium-ion secondary batteries has been rapidly increasing.

In battery modules composed of numerous lithium-ion batteries, the inclusion of abnormal lithium-ion batteries poses a safety risk. One known degradation mode of lithium-ion batteries involves a significant change in electrical double-layer capacitance. By focusing on these differences in electrical double-layer capacitance, it becomes possible to detect abnormal lithium-ion batteries degrading in this mode.

The electric double-layer capacitance of a lithium-ion battery is sometimes described as an electrical circuit including a CPE (Constant Phase Element). A CPE is an element with two constants: a p-constant representing the element's characteristics and a T-constant representing its physical properties. Methods for solving these p-constants and T-constants in the time domain are disclosed, for example, in Patent Document 1 and Non-Patent Document 1.

Japanese Patent Publication No. 2011-145944

Chun-Sing Cheng, Henry Shu-Hung Chung, Ricky Wing-Hong Lau, and Kelvin Yi-Wen Hong, "Time-Domain Modeling of Constant Phase Elements for Simulation of Lithium Battery Behavior," IEEE Transactions on Power Electronics 34(8), 2019, pp 7573-7587.

However, both Patent Document 1 and Non-Patent Document 1 mentioned above had the problem of requiring a lot of computation time when calculating the time-domain behavior of an electrical circuit including a CPE. It is desirable to provide an impedance parameter measurement method and an impedance parameter measurement device that can measure the p constant and T constant while shortening the computation time.

The impedance parameter measurement method relating to the first aspect of this technology is a method for measuring the impedance parameters of an electrochemical device whose equivalent circuit is an electrical circuit including a CPE (Constant Phase Element), and includes the following three elements.
(A) Apply a step-like current change to the electrochemical device. (B) While the voltage of the electrochemical device is undergoing a transient response due to the current change, measure the voltage of the electrochemical device at multiple different timings. (C) Derive the p constant of the CPE based on the multiple voltage values obtained from the measurements, and derive the T constant of the CPE based on the derived p constant and the multiple voltage values obtained from the measurements.

The impedance parameter measuring device relating to the second aspect of this technology is a device capable of measuring the impedance parameters of an electrochemical device whose equivalent circuit is an electrical circuit including a CPE. This impedance parameter measuring device comprises a current source, a measurement circuit, and a signal processing unit. The current source is capable of applying a step-like current change to the electrochemical device. The measurement circuit is capable of measuring the voltage of the electrochemical device at multiple different timings while the voltage of the electrochemical device is in a transient response by applying a current change to the electrochemical device. The signal processing unit is capable of deriving the p constant of the CPE based on the multiple voltage values obtained by measurement, and also of deriving the T constant of the CPE based on the derived p constant and the multiple voltage values obtained by measurement.

In the impedance parameter measurement method relating to the first aspect of this technology, and the impedance parameter measurement apparatus relating to the second aspect of this technology, a step-like current change is applied to an electrochemical device whose equivalent circuit includes an electrical circuit containing a CPE. While the voltage of the electrochemical device is undergoing a transient response, the voltage of the electrochemical device is measured at multiple different timings. Based on the multiple voltage values obtained from the measurements, the p-constant of the CPE is derived, and based on the derived p-constant and the multiple voltage values obtained from the measurements, the T-constant of the CPE is derived. This makes it possible to measure the p-constant and T-constant while reducing the calculation time.

Furthermore, the effects of this technology are not necessarily limited to those described herein, but may include any of the series of effects related to this technology described later.

Figure 1 shows an example of an equivalent circuit of an electrochemical device. Figure 2 shows an example of the voltage response equation for the equivalent circuit in Figure 1. Figure 3 shows an example of the voltage response of the equivalent circuit derived from the voltage response equation in Figure 2, represented on both linear scales. Figure 4 is a diagram showing an example of the voltage response of the equivalent circuit derived from the voltage response equation in Figure 2, on a log-log scale. Figure 3 shows an example of the voltage response of the equivalent circuit derived from the voltage response equation in Figure 2, represented on both linear scales. Figure 4 is a diagram showing an example of the voltage response of the equivalent circuit derived from the voltage response equation in Figure 2, on a log-log scale. Figure 7 is a diagram showing a schematic configuration example of a charge/discharge device according to the first embodiment of this technology. Figure 8 is a diagram illustrating an example of the operation of the charging and discharging device shown in Figure 7. Figure 9 is a diagram showing a schematic configuration example of an impedance parameter measurement system equipped with a server device according to a second embodiment of the present technology. Figure 10 shows an example in which the functions of the temporary storage unit, gradient calculation unit, and Z-parameter calculation unit of Figures 7 and 9 are executed by the control unit.

The embodiments for implementing this technology will be described in detail below with reference to the drawings. The order of explanation is as follows.
1. Background 2. Measurement Principle 3. First Embodiment 4. Second Embodiment 5. Modified Examples

<1. Background＞
In battery modules composed of numerous lithium-ion batteries, the inclusion of abnormal lithium-ion batteries can lead to reduced safety. One known degradation mode of lithium-ion batteries involves a significant change in the electrical double-layer capacity. By focusing on the differences in electrical double-layer capacity, it becomes possible to detect abnormal lithium-ion batteries that degrade in this mode.

The electrical double-layer capacitance of a lithium-ion battery is sometimes described as an electrical circuit including a CPE (Constant Phase Element). A CPE is an element with two constants: a p constant representing its characteristics as an element and a T constant representing its physical properties. The impedance Z in the frequency domain of _{the CPE} is described by the following equation, where j is the imaginary unit and ω is the angular frequency.
Z _CPE =1/{T×(jω) ^p }

Measuring the p-constant and t-constant is useful for distinguishing between abnormal lithium-ion batteries that degrade in the above-mentioned degradation modes and normal lithium-ion batteries. Typically, the AC impedance method is used to measure the p-constant and t-constant. However, AC impedance measurement requires specialized equipment or circuits such as an FRA (Frequency Response Analyzer). Therefore, incorporating such specialized equipment or circuits into electronic devices equipped with battery modules or chargers for charging battery modules has been difficult from a cost perspective.

The following patent documents disclose methods for deriving time-domain solutions to electrical circuits including CPEs using non-integer derivatives (fractional derivatives), rather than integer derivatives such as first or second derivatives. Furthermore, the following non-patent documents disclose methods for deriving time-domain solutions to electrical circuits including CPEs using Laplace transforms.

• Patent document: JP 2011-145944
・Non-patent document: Chun-Sing Cheng, Henry Shu-Hung Chung, Ricky Wing-Hong Lau, and Kelvin Yi-Wen Hong, "Time-Domain Modeling of Constant Phase Elements for Simulation of Lithium Battery Behavior," IEEE Transactions on Power Electronics 34(8), 2019, pp 7573-7587.

However, both the above-mentioned patent and non-patent documents had the problem of requiring a lot of computation time when calculating the time-domain behavior of electrical circuits including CPE. The inventors of this application focused on this problem and propose below an impedance parameter measurement method and an impedance parameter measurement device capable of measuring the p constant and T constant while shortening the computation time.

<2. Measurement Principle>
Figure 1 shows the equivalent circuit of an electrochemical device ED. As shown in Figure 1, the electrochemical device ED is represented by an equivalent circuit that includes a parallel circuit of CPE and a resistor (R). The electrochemical device ED is, for example, a lithium-ion battery (secondary battery), a dye-sensitized solar cell (solar cell), or a fuel cell (electrochemical cell). A current source IS is connected to the electrochemical device ED, and the current I generated by the current source IS is supplied to the electrochemical device ED. If the electrochemical device ED is a lithium-ion battery (secondary battery), the current I generated by the current source IS is supplied to the electrochemical device ED when the electrochemical device ED is fully charged.

The current source IS is capable of providing a step-like current change to the electrochemical device ED. For example, the current source IS can provide a rising-wave current change to the electrochemical device ED as a step-like current change. For example, the current source IS can provide a falling-wave current change to the electrochemical device ED as a step-like current change.

When an electrochemical device ED is supplied with a step-like current change from a current source IS, a transient response occurs in the voltage of the electrochemical device ED. This transient response continues for several tens of microseconds, after which it converges to a constant value. Suppose that the voltage of the electrochemical device ED is measured at multiple (at least two) different timings during the several tens of microseconds in which the voltage of the electrochemical device ED is in a transient response. If a log-log graph of time and voltage is plotted using these multiple voltage values, a linear graph with a slope α is obtained.

Here, the voltage across the CPE in an electrical circuit including a parallel circuit of the CPE and a resistor (R) can be expressed, for example, by the voltage response equation shown in Figure 2 (CSChenge et al., IEEE Trans. on Power Elec. 34(8), 2019, 7573-7587). Using the voltage _νCPE obtained by this equation, if we plot both linear graphs of time and voltage _νCPE , we can obtain graphs like the curve shown in Figure 3. Figure 3 shows examples of graphs when the p constant is fixed at 0.8 and the T constant is 0.1, 0.3, 0.5, 0.7, and 0.9. Furthermore, if we plot both log-log _graphs of time and voltage _νCPE using the voltage νCPE obtained by the above equation, we can obtain graphs like the curve shown in Figure 4. Figure 4 shows examples of graphs when the p constant is fixed at 0.8 and the T constant is 0.1, 0.3, 0.5, 0.7, and 0.9. In Figure 4, it can be seen that the slopes of each graph are approximately equal during the period just before the _CPE voltage ν converges to a constant value.

Furthermore, by plotting both linear graphs of time and voltage _νCPE using the voltage _νCPE obtained by the above equation, a curve graph like the one shown in Figure 5 can be obtained. Figure 5 shows examples of graphs when the T constant is fixed at 0.9Fs ^p-1 and the p constant is 0.5, 0.6, 0.7, 0.8, and 0.9. Moreover, by plotting both log-log graphs of time and voltage _νCPE using the voltage _νCPE obtained by the above equation, a curve graph like the one shown in Figure 6 can be obtained. Figure 6 shows examples of graphs when the T constant is fixed at 0.9Fs ^p-1 and the p constant is 0.5, 0.6, 0.7, 0.8, and 0.9. In Figure 6, it can be seen that the slopes of each graph are different from each other in the period just before the voltage _νCPE converges to a constant value.

Furthermore, the slope α obtained when a step-like current change is applied to the electrochemical device ED coincides with the p-constant when the parallel-connected resistance R can be considered sufficiently large, or when the time evolution of the voltage _νCPE can be considered sufficiently small. This can be explained by the following equation.

According to the above non-patent literature, the voltage transient response of a circuit in which CPE and R are connected in parallel cells can be described by equation (1), where n is the number of steps, T is the step time, C is the T constant of CPE, Φ is the p constant of CPE, and i is the current.

Here, in the case of a step response, we assume that the current i is a constant and that the voltage ν _CPE inside the sigma notation can be considered to be a constant voltage ν _CONST . Alternatively, we assume that R is sufficiently large and ν _CPE / R can be considered to be zero. In this case, the term containing i and ν _CONST can be taken out of the sigma notation. At this point, equation (1) can be transformed into equation (2).

Here, using the relation in equation (3), equation (2) can be transformed into equation (4).

Here, if we change the symbols nT→t (elapsed time), C→T, and Φ→p, equation (4) becomes equation (5). Furthermore, taking the logarithm of both sides of equation (5), we get equation (6). Equation (6) is the equation of a straight line. p is the slope of the log-log plot, and the second term on the right side is the intercept.

From the above, it can be seen that the p-constant can be determined from the magnitude of the slope α obtained when a step-like current change is applied to the electrochemical device ED. Below, we will describe an apparatus that can derive the p-constant using the slope α obtained when a step-like current change is applied to the electrochemical device ED, and then derive the T-constant using the derived p-constant. In the following, we will use a lithium-ion battery as an example of the electrochemical device ED, but the electrochemical device ED is not limited to a lithium-ion battery and may be other devices.

<3. First Embodiment>
[composition]
The configuration of the charge/discharge device 200 according to the first embodiment of this technology will now be described. Figure 7 shows a schematic example of the configuration of the charge/discharge device 200. The charge/discharge device 200 is a device for charging and discharging the secondary battery 100. The charge/discharge device 200 corresponds to one specific example of the "impedance parameter measuring device" according to one embodiment of this technology.

The charge/discharge device 200 not only has the function of charging and discharging the secondary battery 100, but also has the function of measuring the impedance parameters of the secondary battery 100. The "impedance parameters of the secondary battery 100" refer to the p constant and T constant of the equivalent circuit when the equivalent circuit of the secondary battery 100 can be represented by an electrical circuit including a parallel circuit of CPE and a resistor (R).

The secondary battery 100 is a lithium-ion secondary battery. The lithium-ion secondary batteries contained in the secondary battery 100 may be individual cells, battery blocks in which multiple unit cells are connected, or battery packs in which battery blocks and accessories are packaged together. In a battery pack, multiple lithium-ion secondary batteries are connected in series. Within a battery pack, multiple lithium-ion secondary batteries connected in parallel may be included.

The charge/discharge device 200 includes, for example, a charge/discharge circuit 210, a charge/discharge control unit 220, an IV measurement circuit 230, a temporary storage unit 240, a gradient calculation unit 250, a storage unit 260, a Z-parameter calculation unit 270, and an output unit 280, as shown in Figure 7.

The charge/discharge circuit 210 includes a charging circuit for charging the secondary battery 100 and a discharge circuit for discharging the secondary battery 100. The charging circuit includes, for example, a generator and a converter. The charge/discharge control unit 220 is capable of controlling the current for charging the secondary battery 100 and controlling the current for discharging the secondary battery 100. The charge/discharge control unit 220 is composed of, for example, an MPU (Micro-Processing Unit) that performs charge/discharge control, or a CPU (Central Processing Unit) on which a charge/discharge control program is loaded. The charge/discharge control unit 220 is capable of controlling the charge/discharge circuit 210 to provide a step-like current change to the secondary battery 100. For example, the charge/discharge control unit 220 is capable of controlling the charge/discharge circuit 210 to provide a rising-wave current change to the secondary battery 100 as a step-like current change. For example, the charge/discharge control unit 220 is capable of controlling the charge/discharge circuit 210 to provide a falling-wave current change to the secondary battery 100 as a step-like current change.

The charge/discharge circuit 210 can provide a step-like current change to the secondary battery 100 through control by the charge/discharge control unit 220. For example, the charge/discharge circuit 210 can provide a rising-wave current change to the secondary battery 100 as a step-like current change through control by the charge/discharge control unit 220. Alternatively, the charge/discharge circuit 210 can provide a falling-wave current change to the secondary battery 100 as a step-like current change through control by the charge/discharge control unit 220.

The IV measurement circuit 230 includes a measurement circuit capable of measuring the current and voltage of the secondary battery 100. For example, the IV measurement circuit 230 can measure the current and voltage while a transient response occurs in the voltage of the secondary battery 100, given a step-like current change. This transient response lasts for approximately several tens of microseconds, after which it converges to a constant value. The IV measurement circuit 230 can measure the voltage of the secondary battery 100 at multiple (at least two) different timings during the approximately several tens of microseconds while the voltage of the secondary battery 100 is in a transient response. In other words, the period during which the voltage of the secondary battery 100 is measured at multiple (at least two) different timings in the IV measurement circuit 230 is less than several tens of microseconds after the step-like current change is given to the secondary battery 100.

The gradient calculation unit 250 is capable of deriving the slope α on a time-voltage log-log graph based on multiple voltage values obtained by measurements performed by the IV measurement circuit 230. The gradient calculation unit 250 is, for example, composed of a CPU with a program loaded for deriving the slope α.

The memory unit 260 is composed of, for example, volatile memory such as DRAM (Dynamic Random Access Memory), or non-volatile memory such as EEPROM (Electrically Erasable Programmable Read-Only Memory) or flash memory. The memory unit 260 stores, for example, gradient reference values 261. The gradient reference values 261 include a table in which slopes and p-constants are linked to each other. This table contains multiple slopes of different magnitudes and multiple p-constants, one for each slope.

The Z-parameter calculation unit 270 is capable of deriving the p-constant of the CPE of the equivalent circuit of the secondary battery 100 based on the slope α obtained by the slope calculation unit 250. The Z-parameter calculation unit 270 can read the p-constant corresponding to the slope α obtained by the slope calculation unit 250 from the slope reference value 261 of the storage unit 260, and use the read-out p-constant as the p-constant of the CPE of the equivalent circuit of the secondary battery 100.

The Z-parameter calculation unit 270 is capable of deriving the T-constant of the CPE of the equivalent circuit of the secondary battery 100 based on the derived p-constant and multiple voltage values obtained by measurement in the IV measurement circuit 230. The Z-parameter calculation unit 270 can derive the T-constant, for example, using the following formula (see the above non-patent document). Here, ΔI is the change in current before and after the current step, ΔV is the change in voltage after the current step, Δt is the elapsed time after the current step, and Γ is the gamma function.
T=(ΔI/ΔV)×{Δt ^p /Γ(p+1)}

The output unit 280 is an output interface that outputs the impedance parameters (p constant, T constant) obtained by the Z-parameter calculation unit 270 to the outside.

Next, we will explain the measurement of the impedance parameters of the secondary battery 100 in the charge/discharge device 200.

Figure 8 shows an example of the procedure for measuring the impedance parameters of the secondary battery 100 in the charge/discharge device 200. First, the charge/discharge circuit 210 applies a step-like current change to the secondary battery 100 (step S101). Next, the IV measurement circuit 230 applies a step-like current change to the secondary battery 100 and measures the voltage at multiple different timings while the voltage of the secondary battery 100 is in a transient response (step S102).

Next, the gradient calculation unit 250 derives the slope α on a time-voltage log-log graph based on a plurality of voltage values obtained by measurement by the IV measurement circuit 230. Subsequently, the Z-parameter calculation unit 270 derives the p-constant of the CPE of the equivalent circuit of the secondary battery 100 based on the slope α obtained by the gradient calculation unit 250 (step S103). The Z-parameter calculation unit 270 further derives the T-constant of the CPE of the equivalent circuit of the secondary battery 100 based on the derived p-constant and a plurality of voltage values obtained by measurement by the IV measurement circuit 230 (step S104). The output unit 280 outputs the impedance parameters (p-constant, T-constant) obtained by the Z-parameter calculation unit 270 to the outside (step S105). In this way, the impedance parameters of the secondary battery 100 in the charge/discharge device 200 are measured.

[effect]
Next, the effects of the charging and discharging device 200 will be explained.

In this embodiment, a step-like current change is applied to a secondary battery 100 whose equivalent circuit includes an electrical circuit containing a CPE. While the voltage of the secondary battery 100 is undergoing a transient response, the voltage of the secondary battery 100 is measured at multiple different timings. Based on the multiple voltage values obtained from the measurements, the p-constant of the CPE is derived, and based on the derived p-constant and the multiple voltage values obtained from the measurements, the T-constant of the CPE is derived. This allows for the measurement of the p-constant and T-constant while reducing calculation time.

In this embodiment, the p-constant of CPE is derived based on the slope α of a time-voltage log-log graph obtained from multiple voltage values obtained through measurement. This allows for the measurement of the p-constant and T-constant in a short time while reducing calculation time.

In this embodiment, the period for measuring multiple voltage values is less than tens of microseconds after a current change is applied to the secondary battery 100. Thus, in this embodiment, the p-constant and T-constant are derived based on a very short transient response. Therefore, the p-constant and T-constant can be measured in a short time while reducing calculation time.

In this embodiment, a rising-wave current change is applied to the secondary battery 100 as a step-like current change. This allows for the measurement of the p constant and T constant in a short time while shortening the calculation time.

In this embodiment, a step-like current change, specifically a falling-waveform current change, is applied to the secondary battery 100. This allows for the measurement of the p-constant and T-constant in a short time while shortening the calculation time.

<4. Second Embodiment>
Next, an impedance parameter measurement system equipped with a server device 400 as an impedance parameter measurement device according to a second embodiment of this technology will be described. Figure 9 shows a schematic example of the impedance parameter measurement system according to this embodiment.

The impedance parameter measurement system comprises a secondary battery 100, a charge/discharge device 300, and a server device 400. The charge/discharge device 300 and the server device 400 are connected via a communication network 500. The charge/discharge device 300 and the server device 400 are able to communicate with each other via the communication network 500. The communication network 500 includes, for example, the internet, a cloud network, or a network specific to a service provider.

The charge/discharge device 300 is a device for charging and discharging the secondary battery 100 and is a network communication type device that has the function of communicating with an external device. The charge/discharge device 300 includes, for example, a charge/discharge circuit 210, a charge/discharge control unit 220, an IV measurement circuit 230, a communication unit 310, and an output unit 280, as shown in Figure 9. The charge/discharge circuit 210 corresponds to the charge/discharge circuit 210 according to the above embodiment. The charge/discharge control unit 220 corresponds to the charge/discharge control unit 220 according to the above embodiment. The IV measurement circuit 230 corresponds to the IV measurement circuit 230 according to the above embodiment. The communication unit 310 is a communication interface capable of communicating with the server device 400 via the communication network 500. The communication unit 310 is capable of outputting impedance parameters transmitted from the server device 400 to the output unit 280.

The server device 400 includes, for example, a temporary storage unit 240, a gradient calculation unit 250, a storage unit 260, a Z-parameter calculation unit 270, and a communication unit 410, as shown in Figure 9. The temporary storage unit 240 corresponds to the temporary storage unit 240 according to the above embodiment. The gradient calculation unit 250 corresponds to the gradient calculation unit 250 according to the above embodiment. The Z-parameter calculation unit 270 corresponds to the Z-parameter calculation unit 270 according to the above embodiment. The communication unit 410 is a communication interface capable of communicating with the charge/discharge device 300 via the communication network 500. The communication unit 410 is capable of transmitting the impedance parameters obtained by the Z-parameter calculation unit 270 to the charge/discharge device 300.

In this embodiment, the functions of the temporary storage unit 240, the gradient calculation unit 250, the storage unit 260, and the Z-parameter calculation unit 270 are provided in the server device 400. Even in this case, the p-constant and T-constant can be measured while shortening the calculation time, similar to the above embodiment.

<5. Variant Example>
In each of the above embodiments, for example, as shown in Figure 10, the functions of the temporary storage unit 240, the gradient calculation unit 250, and the Z-parameter calculation unit 270 may be implemented by the control unit 320. In this case, the control unit 320 is composed of, for example, an MPU capable of executing the functions of the temporary storage unit 240, the gradient calculation unit 250, and the Z-parameter calculation unit 270, or a CPU into which a program 262 describing a series of operations of the temporary storage unit 240, the gradient calculation unit 250, and the Z-parameter calculation unit 270 is loaded. The program 262 is stored, for example, in the storage unit 260.

In the above embodiments and their variations, the object for which the impedance parameters are to be determined was the secondary battery 100. However, in the above embodiments and their variations, the object for which the impedance parameters are to be determined is not limited to the secondary battery 100, but may be other electrochemical devices.

Furthermore, this technology can also be configured as follows:
<1>
A method for measuring the impedance parameters of an electrochemical device whose equivalent circuit is an electrical circuit including a CPE (Constant Phase Element),
Applying a step-like current change to the electrochemical device,
By applying the current change to the electrochemical device, the voltage of the electrochemical device is measured at multiple different timings while the voltage of the electrochemical device is undergoing a transient response.
An impedance parameter measurement method comprising: deriving the p constant of the CPE based on a plurality of voltage values obtained by the measurement; and deriving the T constant of the CPE based on the derived p constant and the plurality of voltage values obtained by the measurement.
<2>
The impedance parameter measurement method according to <1>, which includes deriving the p constant of the CPE based on the slope of a time-voltage log-log graph obtained from a plurality of voltage values obtained by the above measurement.
<3>
The measurement period is less than or equal to several tens of microseconds after the current change is applied to the electrochemical device. The impedance parameter measurement method according to <1> or <2>.
<4>
An impedance parameter measurement method according to any one of <1> to <3>, comprising applying a rising-waveform current change as the step-like current change to the electrochemical device.
<5>
An impedance parameter measurement method according to any one of <1> to <3>, which includes applying a falling-waveform current change as the step-like current change to the electrochemical device.
<6>
An impedance parameter measuring device for an electrochemical device whose equivalent circuit is an electrical circuit including a CPE (Constant Phase Element),
A current source capable of applying a step-like current change to the electrochemical device,
A measurement circuit capable of measuring the voltage of the electrochemical device at multiple different timings while the voltage of the electrochemical device is undergoing a transient response by applying the current change to the electrochemical device,
An impedance parameter measuring device comprising: a signal processing unit capable of deriving the p constant of the CPE based on a plurality of voltage values obtained by the measurement described above, and deriving the T constant of the CPE based on the derived p constant and the plurality of voltage values obtained by the measurement described above.

The effects described herein are illustrative only; therefore, the effects of this technology are not limited to those described herein. Accordingly, other effects may be obtained with respect to this technology.

Claims (6)

A method for measuring the impedance parameters of an electrochemical device whose equivalent circuit is an electrical circuit including a CPE (Constant Phase Element),
Applying a step-like current change to the electrochemical device,
By applying the current change to the electrochemical device, the voltage of the electrochemical device is measured at multiple different timings while the voltage of the electrochemical device is undergoing a transient response.
An impedance parameter measurement method comprising: deriving the p constant of the CPE based on a plurality of voltage values obtained by the measurement; and deriving the T constant of the CPE based on the derived p constant and the plurality of voltage values obtained by the measurement. The impedance parameter measurement method according to claim 1, further comprising deriving the p-constant of the CPE based on the slope of a time-voltage log-log graph obtained from a plurality of voltage values obtained by the measurement. The impedance parameter measurement method according to claim 1 or claim 2, wherein the measurement period is a period of tens of microseconds or less after the current change is applied to the electrochemical device. The impedance parameter measurement method according to claim 1 or claim 2 , comprising applying a rising-waveform current change as the step-like current change to the electrochemical device. The impedance parameter measurement method according to claim 1 or claim 2 , comprising applying a falling-waveform current change as the step-like current change to the electrochemical device. An impedance parameter measuring device for an electrochemical device whose equivalent circuit is an electrical circuit including a CPE (Constant Phase Element),
A current source capable of applying a step-like current change to the electrochemical device,
A measurement circuit capable of measuring the voltage of the electrochemical device at multiple different timings while the voltage of the electrochemical device is undergoing a transient response by applying the current change to the electrochemical device,
An impedance parameter measuring device comprising: a signal processing unit capable of deriving the p constant of the CPE based on a plurality of voltage values obtained by the measurement described above, and deriving the T constant of the CPE based on the derived p constant and the plurality of voltage values obtained by the measurement described above.